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Right triangle: circumradius and altitude to the hypotenuse given, find the area

The same question, asked 2 times: CDS 2 2020*, CDS 2 2021. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2020

    70
    What is the area of a right-angled triangle, if the radius of the circumcircle is 5 cm and altitude drawn to the hypotenuse is 4 cm ?

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  2. Question 2

    CDS 2 2021

    61
    The radius of circum-circle of a right-angled triangle is 10 cm and the altitude drawn to the hypotenuse is 8 cm. What is the area of the triangle ?

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